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Chapter 2: Q51P (page 45)
A certain ohmic resistor has a resistance of .A second resistor is made of the same material but is three times as long and has half the cross-sectional area. What is the resistance of the second resistor? What is the effective resistance of the two resistors in series?
(i), (ii)
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Apply the general results obtained in the full analysis of motion under the influence of a constant force in Section 2.5 to answer the following questions. You hold a small metal ball of mass m a height h above the floor. You let go, and the ball falls to the floor. Choose the origin of the coordinate system to be on the floor where the ball hits, with y up as usual. Just after release, what are yi and vyi? Just before hitting the floor, what is yf? How much time ∆t does it take for the ball to fall? What is vfy just before hitting the floor? Express all results in terms of m, g, and h. How would your results change if the ball had twice the mass?
A spherical satellite of approximately uniform density with radius\(4.8m\)and mass\(205kg\)is originally moving with velocity\(\left\langle {2600,0,0} \right\rangle m/s,\)and is originally rotating with an angular speed\(2rad/s,\)in the direction shown in the diagram. A small piece of space junk of mass\(4.1kg\)is initially moving toward the satellite with velocity\(\left\langle { - 2200,0,0} \right\rangle m/s.\)The space junk hits the edge of the satellite at location C as shown in Figure 11.97, and moves off with a new velocity\(\left\langle { - 1300,480,0} \right\rangle m/s.\)Both before and after the collision, the rotation of the space junk is negligible.
An object is moving in the + ydirection. Which. If any, of the following statements might be true? Check all that apply. a) the net force on the object is zero. b) The net force on the object is in the - ydirection. c) the net force on the object is in the + ydirection.
On a straight road with the +x axis chosen to point in the direction of motion, you drive for 3 h at a constant 30 mi/h, then in a few seconds you speed up to 60mi/h and drive at this speed for 1 h.
(a) What was the x component of average velocity for the 4 h period, using the fundamental definition. Of average velocity, which is the displacement divided by the time interval?
(b) Suppose that instead you use the equation . What do you calculate for the x component of average velocity?
(c) Why does the equation used in part (b) give the wrong answer?
Because the change of the momentum is equal to the net impulse, the relationship of momentum itself to the net force is somewhat indirect, as can be seen in this question. An object is initially moving in the + x direction with a magnitude of momentum p, with a net force of magnitude F acting on the object in either the + x or - x direction. After a very short time, say whether the magnitude of the momentum increases, decreases, or stays the same in each of the following situations:
a) the net force acts in the + x direction and F is constant.
b) the net force acts in the + x direction and F is increasing.
c) the net force acts in the + x direction and F is decreasing.
d) the net force acts in the - x direction and F is constant.
e) the net force acts in the - x direction and F is increasing.
f) the net force acts in the - x direction and F is decreasing.
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